A queueing system with auxiliary servers
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We examine a queueing system with multiple primary servers and a fewer number of auxiliary servers. There are two classes of customers—those who require service from a primary server working alone and those who require service from a primary server who is assisted by an auxiliary server. Though the apparent Markovian state space is five-dimensional, we show that an aggregation results in an exact two-dimensional representation which is Markovian. Matrix geometric theory is used to obtain approximations for the mean delay and blocking probability of each customer type.
Source: Management Science
Green, Linda. "A queueing system with auxiliary servers." Management Science 30, no. 10 (October 1984): 1207-1216.